Hi i've been struggling over this question for a while. Can anybody help me with this?
A body's velocity at the time t sec is v = 2t^3 - 9t^2 +12t - 5 m/sec. Find the body's speed each time the acceleration is zero.
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What i have been doing is differentiating the finction to find the acceleration with respect to time and setting that equation equal to zero. Once i did that i solved for t(time) and plugged it into the equation that they have in the problem (speed with respect to time).
What am i doing wrong?
It seems like you are on the right track in terms of finding the time when the acceleration is zero and then substituting that time value into the formula for speed. However, there might be a mistake in your differentiation or solving for time steps. Let's go through the steps to solve the problem correctly:
1. Start by differentiating the given equation for velocity v(t) with respect to time.
v(t) = 2t^3 - 9t^2 + 12t - 5
Take the derivative of v(t) to find the acceleration a(t):
a(t) = d[v(t)]/dt = d/dt(2t^3 - 9t^2 + 12t - 5)
2. Set the acceleration equation equal to zero and solve for the time t when the acceleration is zero.
0 = a(t) = d/dt(2t^3 - 9t^2 + 12t - 5)
Differentiate the equation for acceleration a(t) to find the derivative:
0 = d^2[v(t)]/dt^2 = d^2/dt^2(2t^3 - 9t^2 + 12t - 5)
Solve this equation to find the values of t at which the acceleration is zero. These values will correspond to the times when the body has zero acceleration.
3. Once you have determined the time values t when the acceleration is zero, plug each value of t into the equation for speed s(t) to find the body's speed at those specific times.
s(t) = |v(t)| = |2t^3 - 9t^2 + 12t - 5|
Evaluate s(t) for each time value t to get the corresponding speed values.
By following these steps, you should be able to find the times when the acceleration is zero and the body's speed at those times.